# A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus

Research paper by Ilka Agricola, Bernd Ammann, Thomas Friedrich

Indexed on: 09 Dec '98Published on: 09 Dec '98Published in: Mathematics - Differential Geometry

#### Abstract

We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to order 4 upon deformation of the flat metric, study the corresponding Hamiltonian and discuss several families of examples.